We study a critical case of coagulation-fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation, which results from applying the Bernstein transform to the original coagulation-fragmentation equation. Our results include well-posedness, regularity, and long-time behaviors of viscosity solutions to the Hamilton-Jacobi equation in certain regimes, which have implications to well-posedness and long-time behaviors of mass-conserving solutions to the coagulation-fragmentation equation. © 2021 Wiley Periodicals LLC.

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具有乘法凝固核和恒定破碎核的凝固-破碎方程

我们研究了具有乘法凝固核和恒定破碎核的凝固-破碎方程的关键案例。我们的方法基于对新奇异 Hamilton-Jacobi 方程的粘度解的研究，该方程是通过将 Bernstein 变换应用于原始的凝结-破碎方程而产生的。我们的结果包括在某些状态下 Hamilton-Jacobi 方程粘度解的适定性、规律性和长期行为，这对凝结-破碎方程的质量守恒解的适定性和长期行为有影响. © 2021 威利期刊有限责任公司。